A note on a further extension of Gauss’s second summation theorem with an application to the extension of two well-known combinatorial identities

Insuk Kim, Gradimir V. Milovanović*, Richard B. Paris, Arjun K. Rathie

*Corresponding author for this work

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    Abstract

    Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss’s second summation theorem). Our aim in this paper is to establish a further extension of Gauss’s second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth’s old sum (or the Reed Dawson identity) and (ii) Riordan’s identity in the most general form. A few interesting results are obtained as special cases of our main findings.

    Original languageEnglish
    Pages (from-to)959-968
    Number of pages10
    JournalQuaestiones Mathematicae
    Volume45
    Issue number6
    Early online date12 Jun 2021
    DOIs
    Publication statusPublished - 3 Jun 2022

    Keywords

    • Knuth's old sum
    • Reed Dawson identity
    • Riordan identity
    • Gauss second summation theorem
    • Hypergeometric summation formulas and identities

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